Solve the equation given that -9 halves is a zero if -9 halves is a zero. We know that when we do synthetic division, we should get a remainder of 0. So I'm going to put -9 halves in the box. The coefficients across the top bring down the first number, multiply by the number in the box, put it at the next spot over above the line. So then I'm going to add and get -14 multiply by -9 halves and get 63, put it in the next spot over, add, multiply, add. So what this says is I have X - -9 halves times 30 six X ^2 - 14 X -2 equaling 0. Now that's the equivalent of the original equation. If you look here, we could divide A2 out of everything. So X + 9 halves. If I pulled A2 out, if I factored it out, I'd get eighteen X ^2 - 7 X -1 equaling 0. Now I could multiply this two throughout here and get two X + 9 times eighteen X ^2 - 7 X -1 = 0. We want to figure out if this can factor. If we don't want to take the time to factor, we can always use quadratic formula. But two numbers that multiply to give me 18 when multiplying with -1 and +1 to add to give me -7. That actually does factor. So I'm going to have 9X times 2X to give me the 18 X squared. I need it to be a negative 7X. So I'm going to have a -1 down here. So that was negative 9X and a +1 here -9 X +2 X gives me -7 X and a +1 and a -1 gives me that -1. So now if we look at taking each of those terms and setting them equal to 0, we get -9 halves -1 ninth positive 1/2.